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@HastingsMath HastingsMath released this 16 Dec 07:05
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v1.0.1
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MATH NOTES v1.0.1

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Search all AS-LEVEL Pure 1 files

Search all EDEXCEL Pure 1 and 2 files

Search all IEB and DBE CAPS Pure Math Paper 1 and Paper 2 (South Africa) files

Content overview:

  1. Pure Math AS-LEVEL Pure 1 / EdExcel Pure 1 and 2

  2. Stat 1 AS-Level and EdExcel

  3. Pure Math IEB and DBE CAPS (South Africa) Paper 1

  4. Pure Math IEB and DBE CAPS (South Africa) Paper 2

Extended content overview:

1. PURE MATH - (AS-LEVEL PURE 1 / EDEXCEL PURE 1 and 2)

BINOMIAL EXPANSION

OPEN BINOMIAL EXPANSION - With Examples

Includes

  • Introduction to Pascal's triangle
  • Expanding binomials
  • Examples of types of questions
  1. Finding the coefficient of a specific term
  2. Finding the term independent of x
  3. Expanding the binomial
  4. Finding the coefficient of a specific x where r is not given
  5. Finding an extra unknown in the binomial
  6. Two bracket questions
  7. Binomial estimation / approximation
  8. Finding an unknown n using the expansion of ncr

COORDINATE GEOMETRY

OPEN COORDINATE GEOMETRY - QUADRATIC FUNCTIONS

QUADRATIC FUNCTIONS

Includes

  • General from
  • Turning point form
  • X-intercept form
  • Completing the square

CIRCLES, TANGENTS, TRIANGLES

OPEN COORDINATE GEOMETRY - WITH CIRCLES AND TANGENTS AND TRIANGLES PDF

Includes

  • Gradient formula
  • tanx=m
  • Distance formula
  • Midpoint formula
  • Perpendicular lines
  • Parallel lines
  • Straight line formulas
  • Circle formulas
  • Diameter subtends 90 degrees
  • Pythagorus
  • Consecucircles
  • Secant
  • Tangent
  • Center radius form
  • Perpendicular bisectors of chords

FUNCTIONS

EXPONENTIAL AND LOG FUNCTIONS

OPEN FUNCTIONS - EXPONENTIAL AND LOG FUNCTIONS

Includes:

  • Exponential functions introduction, transformations and reflections
  • Log functions as inverse of exponential functions
  • How to graph exponential and log functions
  • Laws of exponents
  • Log laws

INTEGRATION AND DIFFERENTIATION

INTEGRATION AND DIFFERENTIATION 1

OPEN INTEGRATION AND DIFFERENTIATION 1

OPEN CHAIN RULE EXAMPLES

Includes:
Introduction to:

  1. Power rule to differentiate
  2. Reverse power rule to integrate
  3. Chain rule to differentiate
  4. Reverse chain to rule integrate

INTEGRATION AND DIFFERENTIATION 2

OPEN INTEGRATION AND DIFFERENTIATION 2

Includes:

  • Power rule
  • Chain rule
  • Tangents and normal to the curve
  • Stationary points and first derivative (Max/min/point of inflection)
  • Second derivative (concavity/nature of stationary points/ point of inflection)
  • Sketch of the relationship between the curve, first and second derivative
  • Sketching cubic graphs
  • Optimisation / modelling
  • Definite integrals (area / volume)

SEQUENCES AND SERIES

OPEN SEQUENCES AND SERIES - WITH EXAMPLES

Includes:

  • Arithmetic sequences and series
  • Geometric sequences and series
  • Sigma notation
  • Quadratic sequences
  • Examples of the following:
  1. Finding the position
  2. Finding the value
  3. Finding a formula for the nth term
  4. Examples of sigma notation
  5. Examples of the use of simultaneous equations
  6. Finding certain terms in a sequence
  7. Sum to n questions
  8. Sum to infinity questions
  9. Problem solving questions
  10. Problems with extra unknowns in the sequence or series
  11. Recurring decimals proof using sum to infinity

NATURE OF ROOTS

OPEN NATURE OF ROOTS - WITH EXAMPLES

  • Includes notes and examples using the discriminant to comment on the nature of the roots of quadratic functions

POLYNOMIALS

OPEN POLYNOMIALS

Includes:

  1. Factoring cubic functions
  2. Factor and remainder theorem

TRIGONOMETRY

OPEN TRIGONOMETRY 1

Includes:

  • Trig graphs
  • Unit circle
  • Pythagorus
  • Special triangles
  • Area rule
  • Cos rule
  • Sin rule
  • Reduction formulae
  • Co-ratios
  • Cartesian plane quadrants in degrees and radians
  • Converting to degrees or radians
  • Quotient identity
  • Pythagorean identity
  • Double angle formulae
  • Compound angle formulae
  • General solution

OPEN TRIGONOMETRY 2 - CIRCULAR MEASURE

Includes:

  • Arc length
  • Area of a sector
  • Convert radians to degrees
  • Convert degrees to radians
  • Area of a segment

VECTORS

OPEN VECTORS

Includes:

  • What are vectors (summary)
  • Finding vectors
  • Finding the magnitude of a vector
  • Finding unit vectors
  • Adding vectors
  • Subtracting vectors
  • Multiplying vectors
  • Perpendicular vectors
  • Parallel vectors
  • Magnitude-direction form
  • From magnitude-direction form to component form
  • From component form to magnitude-direction form
  • Equal vectors
  • Position vectors
  • The angle between two vectors (scalar product)
  • Positive and negative vectors (quick note)

2. STATISTICS (AS-LEVEL STAT1 / EDEXCEL STAT 1)

-Still to add-

3. PURE MATH IEB and DBE/CAPS NSC (South Africa) Paper 1

FUNCTIONS

FUNCTIONS 1

OPEN FUNCTIONS 1

Includes

  • Linear (straight line) functions and graphs
  • What is a function
  • Types of reflections
  • Quadratic functions (Parabolas)
  • The derivative
  • Finding the formula of a tangent to a quadratic function
  • Inverse of a function
  • Vertical length between functions
  • Average gradient
  • Maximum and minimum length (optimisation)
  • The first and second derivative
  • Points of inflection
  • The relationship between the graphs of f(x), f'(x) and f''(x)
  • Hyperbolic functions

EXPONENTIAL AND LOG FUNCTIONS

OPEN FUNCTIONS - EXPONENTIAL AND LOG FUNCTIONS

Includes:

  • Exponential functions introduction, transformations and reflections
  • Log functions as inverse of exponential functions
  • How to graph exponential and log functions
  • Laws of exponents
  • Log laws

INTEGRATION AND DIFFERENTIATION

INTEGRATION AND DIFFERENTIATION 1

OPEN INTEGRATION AND DIFFERENTIATION 1

OPEN CHAIN RULE EXAMPLES

Includes:
Introduction to:

  1. Power rule to differentiate
  2. Reverse power rule to integrate
  3. Chain rule to differentiate
  4. Reverse chain to rule integrate

INTEGRATION AND DIFFERENTIATION 2

OPEN INTEGRATION AND DIFFERENTIATION 2

Includes:

  • Power rule
  • Chain rule
  • Tangents and normal to the curve
  • Stationary points and first derivative (Max/min/point of inflection)
  • Second derivative (concavity/nature of stationary points/ point of inflection)
  • Sketch of the relationship between the curve, first and second derivative
  • Sketching cubic graphs
  • Optimisation / modelling
  • Definite integrals (area / volume)

SEQUENCES AND SERIES

OPEN SEQUENCES AND SERIES - WITH EXAMPLES

Includes:

  • Arithmetic sequences and series
  • Geometric sequences and series
  • Sigma notation
  • Quadratic sequences
  • Examples of the following:
  1. Finding the position
  2. Finding the value
  3. Finding a formula for the nth term
  4. Examples of sigma notation
  5. Examples of the use of simultaneous equations
  6. Finding certain terms in a sequence
  7. Sum to n questions
  8. Sum to infinity questions
  9. Problem solving questions
  10. Problems with extra unknowns in the sequence or series
  11. Recurring decimals proof using sum to infinity

NATURE OF ROOTS

OPEN NATURE OF ROOTS - WITH EXAMPLES

  • Includes notes and examples using the discriminant to comment on the nature of the roots of quadratic functions

POLYNOMIALS

OPEN POLYNOMIALS

Includes:

  1. Factoring cubic functions
  2. Factor and remainder theorem

FINANCIAL MATH

OPEN FINANCIAL MATH

Includes:

  • Simple growth / decay
  • Compound growth / decay
  • Future value
  • Present value
  • Effective interest
  • Other useful notes and terminology
  • Balance outstanding
  • Delay start questions

PROBABILITY
-still to add-

4. PURE MATH IEB and DBE/CAPS NSC (South Africa) Paper 2

TRIGONOMETRY

OPEN TRIGONOMETRY 1

Includes:

  • Trig graphs
  • Unit circle
  • Pythagorus
  • Special triangles
  • Area rule
  • Cos rule
  • Sin rule
  • Reduction formulae
  • Co-ratios
  • Cartesian plane quadrants in degrees and radians
  • Converting to degrees or radians
  • Quotient identity
  • Pythagorean identity
  • Double angle formulae
  • Compound angle formulae
  • General solution

COORDINATE GEOMETRY

OPEN COORDINATE GEOMETRY - QUADRATIC FUNCTIONS

QUADRATIC FUNCTIONS

Includes

  • General from
  • Turning point form
  • X-intercept form
  • Completing the square

CIRCLES, TANGENTS, TRIANGLES

OPEN COORDINATE GEOMETRY - WITH CIRCLES AND TANGENTS AND TRIANGLES PDF

Includes

  • Gradient formula
  • tanx=m
  • Distance formula
  • Midpoint formula
  • Perpendicular lines
  • Parallel lines
  • Straight line formulas
  • Circle formulas
  • Diameter subtends 90 degrees
  • Pythagorus
  • Consecucircles
  • Secant
  • Tangent
  • Center radius form
  • Perpendicular bisectors of chords

EUCLIDEAN GEOMETRY

CIRCLE GEOMETRY

[OPEN CIRCLE GEOMETRY]https://github.com/HastingsMath/mathnotes/blob/120687933dcabfc6b7145417d639f8eeeef6889b/CAPS%20and%20IEB%20NSC%20(SOUTH%20AFRICA)/PURE%20MATH/Paper%202/EUCLIDEAN%20GEOMETRY%20-%20CIRCLE%20GEOMETRY.pdf

Includes

  • Summary of circle theorems
  1. line from center to midpoint chord
  2. angle at center equals two times angle at circumference
  3. angles subtended by equal chords
  4. equal chords subtend equal angles
  5. opposite angles of a cyclic quad are supplementary
  6. lines of tangents that meet at a single point are equal in length
  7. tan-chord theorem
  8. proving cyclic quadrilaterals
  9. radius perpendicular to tangent
  10. angles on diameter
Assets 2
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